Methods for quantifying the morphology and amplitude of cardiac action potential alternans

ABSTRACT

Methods and apparatus for determining T-wave alternan signatures (i.e., morphology and polarity) derived from a physiologic signal representative of a subject&#39;s heart activity; assessing changes in the myocardium Action Potential (“AP”) through analysis of the alternan signature derived from a physiologic signal representative of a subject&#39;s heart activity; and/or assessing spatial disassociation of alternan characteristics that are likely associated with the initiation of re-entrant arrhythmias.

TECHNICAL FIELD

The present invention relates to methods and apparatus for determiningT-wave alternan signatures (i.e., morphology and polarity) derived froma physiologic signal representative of a subject's heart activity;assessing changes in the myocardium Action Potential (“AP”) throughanalysis of the alternan signature derived from a physiologic signalrepresentative of a subject's heart activity; and/or assessing spatialdisassociation of alternan characteristics that are likely associatedwith the initiation of re-entrant arrhythmias.

BACKGROUND

T-wave alternans are characterized by a pattern of alternations in theamplitude of the T-wave component of an ECG, where the even beatssystematically display a different amplitude than the odd beats (an“ABABAB . . . ” pattern of beat signatures). Many prior research effortshave found correlations between the amplitude of the T-wave alternansduring periods of increased heart rates, and sudden cardiac arrest orarrhythmias. Verrier and Cohen, in their chapter “Risk Identification byNoninvasive Markers of Cardiac Vulnerability” (Foundations of CardiacArrhythmias, Spooner and Rosen editors, Marcel Dekker, Inc., 2000),provide an overview of past research and describe a signal processingmethod for determining the presence of microvolt level alternans.Summarily stated, the ECG signal is evaluated to identify sequentialdata points within the T-waves. The amplitude of these selected points,from successive beats, forms pseudo time series that are next subjectedto Fourier analysis to create a power spectrum; the power at the Nyquistfrequency of this spectrum provides an estimate of the energy of thebeat-to-beat fluctuations in the amplitude of the T-wave. The powerspectra from successive individual spectra associated with differentoffset times within the T-wave coda are averaged to establish acomposite power spectra, which is claimed to be useful in assessingpatient risk for sudden cardiac arrest or arrhythmias. Clinicalobservations and trials have shown that persons who exhibit T-wavealternans at relatively low heart rates, i.e., ˜110 bpm, are at greaterrisk of developing fatal arrhythmias than those who exhibit alternans atheart rates approaching their maximum target heart rate. Both thispublication, as well as U.S. Pat. Nos. 4,802,491; 5,148,812; and5,713,367 relating to this and related approaches are incorporatedherein by reference.

While the above-described method may be valuable for establishing thegross existence and severity of T-wave alternans, the analysis islimited to only the average amplitude of the alternan signal across theentire T-wave signal. Clinical experience with stratifying patient riskof sudden cardiac death based upon this simplistic characterization ofthe alternan signal are typified by a high rate ofindeterminacy—typically as high as 30% of the patient tests foralternans are indeterminate.

SUMMARY

The invention is broadly directed to cardiac assessments derived throughT-wave analysis. Additional information contained within the alternansignal may yield important insight into the electrophysiology of themyocardium, including parameters that quantify the phase of the ActionPotential (“AP”) that is exhibiting an alternating pattern and thedegree of zonal disassociation across the heart (i.e.: out of phasealternans across the heart that may be the source trigger for re-entrantarrhythmias). These additional data may lead to an improved method forpatient risk stratification and a lower indeterminate threshold. Variousfeatures of the invention are directed to methods for determining T-wavealternan signatures (i.e., morphology and polarity) derived from aphysiologic signal representative of a subject's heart activity;assessing changes in the myocardium Action Potential (“AP”) throughanalysis of the alternan signature derived from a physiologic signalrepresentative of a subject's heart activity; and/or assessing spatialdisassociation of alternan characteristics that are likely associatedwith the initiation of re-entrant arrhythmias.

As will be discussed in more detail below, some or all of these featurescan be used to assess the cardiac condition of a subject. In allembodiments, an estimated T-wave alternan signature for a given heartrate is needed. This estimated T-wave alternan signature includesderived waveform morphology (signal) while preserving the polarity ofthe waveform, which provides data heretofore unavailable by the priorart methods of cardiac assessment through T-wave analysis. Robustembodiments include multiple T-wave alternan estimates for multipleheart rates across at least one signal source, such as at least oneconventional ECG Stress test lead.

In certain embodiments, a physiologic signal representative of asubject's heart activity is acquired and the T-wave component ofselected heartbeats is identified. The T-wave components of adjacentheartbeats are differenced to obtain a gross estimate of resultantalternan signatures. The gross estimate is constructed to include andpreserve amplitude polarity information. At least one and preferablyseveral signal processing functions are performed to derive at least onedesired alternan signature estimate for the selected heart beats, whichis statistically correlated to and representative of the alternansignature of the selected heart beats.

The derived alternan estimate is preferably one of many such estimatesrepresentative of various cardiac conditions induced by stress testingthe subject. A feature of an embodiment of the invention relates to thereporting of the derived data. For example, an embodiment of a reportingfeature includes the simultaneous visual display of a plurality ofderived alternan signature estimates in matrix form. In such anembodiment, the plurality of derived alternan estimates are associatedwith a corresponding plurality of heart rates by displaying temporallyadjacent estimates adjacent to one another. In this manner, an analystis readily able to discern changes in the alternan waveform morphologyover the range of heart rates being reported. Moreover, the reportingfeature can further include simultaneously displaying visualrepresentations, either numerically or graphically, of the relativealternan waveform amplitudes derived from each physiologic signal. Forexample, a plurality of alternan waveform estimates derived from aplurality of ECG leads are presented in such a format.

Another feature of several embodiments of the invention is to normalizethe acquired data to provide a better correlation between the alternanestimate and the actual heart condition. Motion artifacts, muscleartifacts, system noise, respiratory artifacts or other noise present inat least one physiologic signal representative of a subject's heartactivity can obscure the alternan estimate. To mitigate such noise, theacquired data is normalized so that the alternan estimate more closelycorrelates to the actual condition of the subject's heart. In oneembodiment of the normalization procedure, systemic amplitudefluctuations and baseline wander in the waveform are characterized. Theassociated effects on the signal are then minimized by correcting foramplitude gain and DC bias to achieve a more accurate alternan estimatefor a plurality of repeating waveforms.

Several embodiments of the invention also increase the real-timereporting ability of certain results and reduce random or stationarynoise by smoothing and sub-sampling the gross alternan estimates. Suchnoise reduction can be achieved by calculating median or average valuesand curve fitting using first or second order polynomials. In apreferred embodiment, time domain segments (time bins) of a givenalternan estimate are established, which preferably reduce the number ofdata points to about 15 to 25. Suitable noise reduction algorithms, suchas those described above, are applied to each time bin, thereby yieldinga smoothed estimate of the alternan signature of interest. This methodis then applied to a suite of temporally adjacent alternan estimatesuntil a desired number of alternan estimates have been derived.

The usefulness of the smoothed alternan estimates can be enhanced byobtaining a reference curve from these estimates, such as by averagingthe curves or preferably finding the median curve. From this referencecurve, a weighting factor can be established and used to determined aweighted average alternan estimate of the suite of smoothed alternanestimates derived above. In a specific embodiment, the root mean square(RMS) of the difference between the reference curve and each of thesmoothed T-wave alternan estimates from the suite of heartbeats isdetermined. Smoothed alternan estimates that are similar to thereference curve, i.e., those wherein the RMS value is small, areweighted more heavily than those that are dissimilar to the referencecurve, i.e., those wherein the RMS value is large. The derived weightingfactor is then applied to each alternan estimate and the weightedsmoothed estimates averaged to yield a robust alternan estimate for thesuite of heartbeats under consideration, or portions thereof.

Yet another feature of several embodiments of the invention manages orotherwise compensates for disruptive events, such as premature beats,pauses or other disruptions to a steady cardiac rhythm, that may reversethe polarity of the alternan signature. Adjustment for the presence ofdisruptive events is generally desirable for many polarity sensitiveembodiments of the invention. By monitoring the polarity of eachalternan signal within a suite of heartbeats, adjustments to thepolarity of alternan estimates following a disruptive event can beapplied.

Still another feature of a specific embodiment provides a basis forassociating certain types of alternan signatures with physiologicalchanges in the action potential (AP) of a subject's heart. It has beenfound that a relationship exists between epicardial AP alternations andT-wave alternans. For example, the three major forms of epicardial APalternations, i.e., depolarization, refractory, and repolarizationphases, are associated with three distinct T-wave alternan signatures.An aspect of this feature is to ascertain data from the T-wave alternanestimates that represent specific characteristics of AP alternations. Inone embodiment, at least three model curves are established thatrepresent the alternation in ECG signal associated with alternation ineach phase of the AP. Through a simultaneous curve fitting method, theestimated alternan signal is decomposed into components representing thecontribution from each of the three distinct AP processes. Thus, byanalyzing the waveform of a T-wave alternan estimate, one is providedwith information regarding the affected phase of the epicardial AP. Riskestimates of cardiac instability may be developed from these distinctestimates of AP alternation.

Preserving the full waveform of the alternan signal, including recordingconsistent amplitude polarity, supports an assessment of cardiacalternan disassociation wherein distinct regions of the heart displaydifferent alternan characteristics. These out-of-phase alternan patternsestablish voltages across regions of the heart and may triggerarrhythmias. A risk assessment method can then be developed thatquantifies the severity of the alternan disassociation based upon thesimultaneous voltage differences of the alternan signatures and thespatial separation of the regions sampled by the distinct physiologicsignals.

An embodiment of one method for determining T-wave alternan signaturesin accordance with the invention comprises: (1) acquiringelectrophysiological data (a beat series) from a subject's heart ofsufficient duration wherein such data includes electrical signalscorresponding to T-wave data found in an electrocardiogram (“ECG”); (2)identifying T-wave segments within the beat series data for use in theanalysis that account for ectopic beats and other significant changesthat may disrupt the alternan pattern; (3) correcting the data forbaseline wander and motion artifacts associated with respiration andother noise; (4) differencing adjacent beats within the beat serieswhile retaining polarity and morphology information to compute initialestimates of the alternan signature for the series; and (5) smoothingand stacking the individual estimates to lower noise and provide arobust estimate of the alternan signature for the beat series. Thismethod can further comprise (6) decomposing the alternan signature intocomponents related to changes in the depolarization, refractory andrepolarization components of the myocardium AP; and/or (7) reporting thealternan signatures. In addition, optional procedures can be employed toassess the severity of spatial disassociation of the alternan signaturein other embodiments of methods in accordance with the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a flow chart illustrating a method for determining andrepresenting a T-wave alternan estimate in accordance with an embodimentof the invention.

FIG. 1B is a diagram schematically illustrating stages of the method fordetermining and representing an alternan estimate in accordance with theembodiment of the invention shown in FIG. 1A.

FIG. 2A is a graph illustrating an ECG and the reference pointscorresponding to activation and recovery of the Atria (P); the ventricleactivation phases Q, R and S, forming the QRS complex; the recovery orre-polarization phase T of the ventricles; and the R-R time intervalbetween consecutive beats as measured between the peaks of the R phase.

FIG. 2B is a graph showing the alignment of QRS complexes from across-correlation.

FIG. 3 is a graph illustrating a sample ECG Beat Sequence and a computedMedian beat in accordance with an embodiment of the invention.

FIG. 4 shows the alignment of the P-S signature of the average beat(Ave(i)) with the beat sequence and the resulting amplitude and DCoffsets (G and C respectively) that mitigates the RMS error between theaverage and the beat sequence in accordance with an embodiment of theinvention.

FIG. 5 is a graph illustrating the computed gain for a sequence of beatsthat mitigates the amplitude and baseline wander associated with therespiration signal contained in the ECG in accordance with an embodimentof the invention.

FIG. 6 is a schematic illustration showing an example of overlappingwindows used to bin and smooth the alternan estimate data in accordancewith an embodiment of the invention.

FIG. 7 is a graph showing sixteen individual smoothed estimates ofalternan signature computed from 17 successive beats in accordance withan embodiment of the invention.

FIG. 8A is a diagram showing the estimates of smoothed alternansignatures computed from 16, 32 and 64 alternan estimates fromsuccessive beats in accordance with an embodiment of the invention.

FIG. 8B is a graph illustrating an ECG signal interrupted by ectopicbeats, dividing the entire sequence into multiple segments of contiguousbeats.

FIG. 8C is a diagram showing the polarity reversal of the smoothedalternan estimate that may occur when an ectopic beat or otherdisruption to the heart rhythm occurs.

FIG. 9 is a graphic overlay of APs and T-wave formation wherein theT-wave represents the difference between the endocardial and epicardialAPs in accordance with an embodiment of the invention.

FIG. 10 is a graph illustrating an alternan signal associated withamplitude alternans in the depolarization phase of the epicardial AP inaccordance with an embodiment of the invention.

FIG. 11 is a graph illustrating an alternan signal associated withalternans in the epicardial refractory period of the AP in accordancewith an embodiment of the invention.

FIG. 12 is a graph illustrating an alternan signal associated withalternans in the epicardial repolarization phase the AP in accordancewith an embodiment of the invention.

FIG. 13 is a diagram illustrating the parametric form of three curvesused to decompose the alternan signature into the three phases of theassociated AP in accordance with an embodiment of the invention.

FIG. 14 is a graph illustrating an example of color coding correspondingto the amplitude of the alternan signature in accordance with anembodiment of the invention.

FIG. 15 is a representation of a composite display of the alternansignature for an entire stress test, including data for 8 independentECG leads in accordance with an embodiment of the invention.

FIG. 16 is a graph showing a possible display of average alternanamplitude and heart rate for a stress test in accordance with anembodiment of the invention.

DETAILED DESCRIPTION

The following discussion is presented to enable a person skilled in theart to practice the invention. Various modifications to the disclosedembodiments will be apparent to those skilled in the art, and thegeneric principles herein may be applied to other embodiments andapplications without departing from the spirit and scope of the presentinvention as defined by the appended claims. Thus, the present inventionis not intended to be limited to the embodiments presented, but is to beaccorded the widest scope consistent with the principles and featuresdisclosed herein.

FIG. 1A is a flow chart of a method 100 for determining and representinga T-wave alternan estimate in accordance with an embodiment of theinvention, and FIG. 1B is a diagram schematically illustrating thestages of the method 100 shown in FIG. 1A. Referring to FIGS. 1A and 1Btogether, the method 100 includes a first stage 102 comprising acquiringelectrophysiological data (e.g., a heartbeat series) of sufficientduration to include electrical signals corresponding to T-wave data. Themethod 100 also includes a second stage 104 comprising identifying theT-wave segments within the series of heartbeats. The second stage 104,for example, can further include assessing the identified T-wavesegments to compensate for ectopic beats and other significant changesthat may disrupt the alternan pattern. Referring to FIG. 1B, the firststage 102 and second stage 104 are graphically illustrated using anelectrocardiogram (ECG) readout in which the T-wave segment isidentified for sequential heartbeats A and B by bracketed arrows.

The method 100 continues with a third stage 106 that includes correctingthe acquired data for baseline wander and motion artifacts caused byrespiration, movement and other sources of noise. The third stage 106 inFIG. 1B graphically illustrates subsequent T-wave segments that havebeen corrected for baseline wander and artifacts caused by such noise.After the third stage 106, the method includes a fourth stage 108 inwhich initial estimates of the alternans between subsequent beats arecalculated, and a fifth stage 110 in which the estimated initialalternans are smoothed and stacked to further lower the noise andprovide a more robust estimate of the alternan signature for a series ofheartbeats. The fourth stage 108 can include computing the initialestimate of the alternans by calculating the differences betweenadjacent T-wave segments within the beat series at common respectivetime intervals in a manner that retains the polarity and morphologyinformation. The fifth stage 110 can further include (a) providing amedian estimate, (b) weighting the median estimate, and then (c)determining a weighted average estimate of An alternans.

The method 100 can optionally include a sixth stage 112 comprisingdecomposing the alternan signature into components related to changes inthe (a) depolarization, (b) refractory, and (c) repolarizationcomponents of the myocardium action potentials (AP). The sixth stage 112can accordingly determine different action potential decompositionsrelative to the weighted alternan average An to provide specificinformation to evaluate a patient as described in more detail below.Several embodiments of the method 100 also include a seventh stage 114in which the alternan signatures for various electrodes are reported toan operator. As shown in FIG. 1B, the seventh stage 114 can report thealternan signatures in a graphical display illustrating the weightedaverage alternan estimate An for a number of electrodes during a stresstest. An eight stage 116 further processes the data from stage 110, forall leads and all time intervals, to derive a measure of spatialdisassociation of alternan voltages for use in assessing patient riskfrom arrhythmias.

The embodiment of the method 100 shown in FIGS. 1A-1B is broken downinto discrete steps illustrating one embodiment of a series of stepsthat achieve certain benefits of the invention. Other embodiments ofmethods in accordance with the invention may not include all of thestages 102-116 and still achieve several benefits of the embodimentshown in FIGS. 1A-B. For example, if suitable digital ECG data isalready available, it is not necessary to create the data and certainsteps need not be performed in order to achieve the benefits of theinvention. The following discussion accordingly describes several of thestages 102-116 of the method 100 in greater detail with theunderstanding that the individual stages can be eliminated or use otherprocesses in other embodiments of the invention.

A. Data Source and Protocol

The first stage 102 of the embodiment in this method 100 shown in FIG.1A involves acquiring electrophysiological data from a data source usinga suitable protocol. Clinically useful estimates of low amplitudealternan signals preferably require a contiguous heartbeat series of64-128 beats with an approximately constant heart rate. The number ofcontiguous beats may be in the range of 16-32 in the presence of lownoise, and in exceptional conditions could be as low as 2 beats. Becauseof the very low voltages being analyzed, robust methods for reducingnoise at all stages of data acquisition and processing is highlydesirable. While some sources of noise cannot be reduced (see below),good ECG electrode preparation such as with Quinton Cardiology Inc.'sQUICKPREP® will significantly reduce the level of noise relating to theelectrode-subject interface. Details of this product and related methodsof use can be found in commonly owned U.S. Pat. No. 5,458,141, which isincorporated by reference. In addition or alternatively, monitoring ofelectrode impedance and noise during application will contribute tooverall noise reduction.

Noise directly affects the length of the beat series used to computealternan estimates. Stationary noise not linked with or created by thebeat should decline approximately as the square root of the number ofbeats included in the series—e.g.: 16 beats should lower the noise byabout a factor of 4, and 64 beats should lower noise by about a factorof 8. A dynamic assessment of noise conditions during data acquisitionand processing can be used to establish the number of beats necessary toprovide reliable data. Because ectopic beats and other cardiac events(e.g., a pause or a rapid change in R-R interval) can disrupt thealternan pattern, minimizing the number of consecutive beats required toobtain reliable results affords more opportunity for diagnosis ofsubjects with higher incidences of ectopic heart beats.

Noise can be generated from a multiplicity of sources and therefore theidentification and suppression, conditioning and/or filtering of suchnoise is desirable. Common sources of subject-related noise includemotion artifacts (movement of the heart within the pericardial cavity orchest movement induced by body impacts encountered from walking orrunning during a treadmill stress test); surrounding muscle contractionartifacts from body and arm motion; breathing or respiration artifacts(both from the change in chest impedance and the repositioning of theheart within the chest as the lungs inflate); and, electrode-skincontact noise.

Some subject-related noise suppression and/or conditioning is relativelyeasy to achieve and include actions such as having the subject minimizeand/or keep constant the rate of body impacts during testing;maintaining a constant rate of physical exertion (e.g., a constant paceof walking on a treadmill); attempting to maintain a relatively constantrespiration rate; etc. The conditioning generally attempts to eliminateor stabilize the frequency, duration, and/or amplitude of the noise,which facilitates noise identification and removal. Thus, increasing therate of physical exertion during stress testing by having the subjectmaintain a constant pace while increasing the elevation of a treadmillis one means for conditioning the noise for later filtering (and thussuppressing the effect of that noise). A derivative of this approach isto monitor the heart rate and dynamically adjust the grade of thetreadmill to maintain the target rate, thereby eliminating the variablesassociated with a non-stable heart rate during the data acquisitionphase.

In addition to external sources of noise, there is clinical/laboratorydata that suggests ectopic beats and other cardiac events may re-set thealternan signal (i.e., the alternan signal may shift a beat, switchingfrom an even-odd pattern to an odd-even pattern, thus disrupting theanalysis). Therefore, contiguous beat sequences should be selected foranalysis that exclude ectopic beats or other disruptions. For subjectswith a high ectopic rate it is necessary to extend the analysis bycombining multiple shorter beat sequences and using correlation methodsto determine the possible polarity change for each sequence associatedwith a changing beat pattern, as discussed below.

A preferred stress profile to induce an alternan response is to place asubject on a controllable, variable speed treadmill with a variableincline feature such as the Q-Stress® cardiac stress testing systemmanufactured by Quinton Cardiology, Inc. The data acquisition protocolis preferably similar to a standard Burke protocol, beginning with thesubject at rest and recording a suite of heartbeats for about 2-3minutes. Next, the subject's heart rate is increased by increasing thetreadmill grade and then held constant for about 2-3 minutes, duringwhich time another suite of heartbeats is recorded. This progressioncontinues until the desired maximum heart rate is achieved or thesubject is exhausted. Maintaining a constant treadmill speed, and thus aconstant pace, while increasing the grade stabilizes noise associatedwith body motion artifacts and improves the estimate of alternansignature associated with increasing heart rate. Alternatively, but withsomewhat higher motion noise associated with increasing heart rate,other protocols such as the Bruce protocol could be used to exercise thesubject, where both the speed and grade are adjusted periodically untilthe subject either reaches the desired maximum heart rate or isexhausted.

B. Cross-Correlation and T-Wave Selection

After successfully recording appropriate ECG samples or retrieving suchsamples from stored data at each desired heart rate, the method 100continues with the second stage 104 by ascertaining the alternancomponent between temporally adjacent T-waves. One aspect of this stageis consistently selecting from beat to beat the onset time of the T-wavesegment. The amplitude of the T-wave is very large compared to thealternan heartbeats signal. In general, the T-wave may have an amplitudeof 300-1000 microvolts; the alternan signal computed from the differenceof adjacent T-waves may have an amplitude of only a few microvolts. Amis-alignment of the T-wave between two adjacent beats of 2.0milliseconds (the standard sampling rate for stress testing) can producea false amplitude anomaly of 5-10 microvolts. Therefore, it is importantto use a high sampling rate, e.g., 0.5-1.0 millisecond, and toaccurately align the T-waves in order to measure the signal and not beoverwhelmed by processing noise associated with mis-alignment of theT-waves from beat to beat.

FIG. 2A illustrates an example ECG with the key phases identified. Thenormal heart beat starts in the upper chambers of the heart (atria) andthe initial ECG phase that records this activation is termed the P-wave;the bracket indicates the duration of the P-wave. Following theactivation of the atria the blood moves into the lower chambers of theheart (ventricles) and activation of the ventricle muscle both pumps theblood to the body and generates the ECG phases Q, R and S, oftenreferred to as the QRS complex. Finally, the ventricle muscles recover(repolarize) in anticipation of the next beat, creating the T-wavesignal on the ECG. The time interval between adjacent beats is generallymeasured between the peaks of the R-wave and is referred to as the R-Rinterval. The letter designations are commonly used to also specifyspecific segments of the ECG. For instance, the PQ interval would be thesegment that begins with the onset of the P-wave and concludes with theQ-wave.

FIG. 2B illustrates an example of aligned waveforms from a series ofheartbeats. The waveforms have a QRS complex 202 with an R-wave peak204. For a sequence of beats to be analyzed for an alternan signal, thefollowing steps are preferably used to select the T-wave segment withineach beat in a beat series.

-   -   1. Using the R-wave peak 204 within the QRS complex 202 to        approximately time align each beat, compute a median beat        estimate for the selected sequence of beats for at least one,        and preferably all, ECG leads.    -   2. Window the QRS segment from the median beat estimate computed        in step 1 and cross-correlate this windowed QRS pulse with the        ECG data, finding the peaks in the cross-correlation.        Preferably, the cross correlation metric should be based upon        the peak of the sum of the cross correlations across leads I,        II, and V1-V6—i.e.: the selected QRS correlation time point        should be the same across all leads.    -   3. Use the refined QRS onset time from step 2 to re-stack the        data, using either an average or median stack, thus developing        an improved estimate of the QRS complex.    -   4. Using the improved QRS estimate, repeat steps 2 and 3 above,        resulting in a final estimate of QRS onset time for all beats in        the sequence and all traces and a best estimate of the QRS        complex morphology. Save the QRS complex for further use in        computations discussed below.    -   5. The T-wave 210 for each lead is preferably selected based on        the following parameters:        -   a. The onset time should be a few samples beyond the maximum            negative excursion of the S-wave 212 (and the same across            all leads).        -   b. The duration of the T-wave, and hence the end time, is            more complex. Preferably, the analysis uses the entire            T-wave, but it is helpful to maintain a constant T-wave            window length over the entire test analysis. As heart rate            increases, the P-wave for the next beat may start to ride on            the end of the T-wave from the previous beat, adding noise            to the analysis. The target heart rate and the associated            estimate of the duration of the R-R interval (D_(R-R)) at            peak exercise, along with the duration of the interval from            the onset of the P wave to the end of the S phase (D_(P-S)),            should be used to compute a maximum window length for the            T-wave (Maximum Length=D_(R-R)−D_(P-S). The T-wave window            length should be computed from the initial (resting) data            and held constant for the entire test. Preferably, the end            of the windowed T-wave should be well beyond the peak of the            T-wave—as discussed below, most of the alternan signal will            be in the segment between the end of the S-wave and the peak            of the T-wave.

The cross-correlation times of the QRS complex also form the basis fortracking R-R intervals and associated dispersion, and for identifyinganomalous pauses or jumps in heart rate that may re-set the alternansignal. The cross-correlation times are useful in this analysis and aregenerally retained for subsequent use.

C. T-Wave Normalization for Baseline Wander

The third stage 106 of the method 100 processes the data to mitigate theaffects of noise. The ECG data is influenced by many sources of noise,including high frequency muscle artifact and system noise as well aslong period noise associated with respiration and body movements.Referring to FIG. 3, the raw ECG data typically includes both a baselinewander and amplitude variations associated with respiration. In thisfigure the amplitude variations can be seen by examining the differencebetween the peak of the R-wave and the trough of the S-wave; thisdifference is smallest for the beats on the left and right side of thefigure and maximum for the beats in the central portion of the ECG. Thisfigure also illustrates baseline wander as detected by observing how theonset of the QRS complex rises for the central beats and falls for thebeats on the left and right sides of the ECG. Even though the ECG dataincludes such baseline wander and amplitude variations, a robustestimate of the average or median beat, Ave(i), can be computed, asdiscussed in the previous section, and is shown adjacent to the ECGtrace.

The average or median beat Ave(i) estimate can be compared with theindividual beats to derive an amplification gain factor and a DC shiftfactor. For example, the median or average beat, Ave(i), can be scaledby an amplification factor G(m) and DC shift factor C(m) to minimize theleast square difference with each beat in the sequence. To mitigate orprevent introducing systematic bias or noise into the T-wave portion ofthe signal, the minimization window should focus on just the P-S beatsegment and solve for the optimal G and C for each beat, as illustratedin FIG. 4.

The system of equations to be solved for each beat are:G×Ave(i)+C=ECG(i)In matrix notation the least squares solution to this system ofequations is: $\begin{pmatrix}G \\C\end{pmatrix} = {\begin{pmatrix}{\sum\limits_{n}{{Ave}^{2}(i)}} & {\sum\limits_{n}{{Ave}(i)}} \\{\sum\limits_{n}{{Ave}(i)}} & n\end{pmatrix}^{- 1}\begin{pmatrix}{\sum\limits_{n}{{{Ave}(i)}{{ECG}(i)}}} \\{\sum\limits_{n}{{ECG}(i)}}\end{pmatrix}}$where n is the number of data points in the P-S interval. Solving forthe inverse yields:$G = \frac{{n{\sum\limits_{n}{{{Ave}(i)}{{ECG}(i)}}}} - {\sum\limits_{n}{{{Ave}(i)}{\sum\limits_{n}{{ECG}(i)}}}}}{{n{\sum\limits_{n}{{Ave}^{2}(i)}}} - ( {\sum\limits_{n}{{Ave}(i)}} )^{2}}$$C = \frac{{\sum\limits_{n}{{{Ave}^{2}(i)}{\sum\limits_{n}{{ECG}(i)}}}} - {\sum\limits_{n}{{{Ave}(i)}{\sum\limits_{n}{{{Ave}(i)}{{ECG}(i)}}}}}}{{n{\sum\limits_{n}{{Ave}^{2}(i)}}} - ( {\sum\limits_{n}{{Ave}(i)}} )^{2}}$

Once G and C are derived for each beat, a cubic polynomial function(F_(C) and F_(G)) can be computed that smoothly connect four values of Gor C associated with four consecutive beats. The computed middle segmentof the resulting function, between the second and third values for G orC, is used to correct for gain and DC bias for the T-wave in thissegment, following:${{ECG}_{corrected}(i)} = \frac{{{ECG}(i)} - {F_{C}(i)}}{F_{G}(i)}$

As noted by many previous investigators (see, e.g., Moody et al.,“Clinical Validation of the ECG-Derived Respiration (EDR) Technique,”Computers in Cardiology, p 507-510, 1986, which is incorporated byreference), the ECG signal is modulated by respiration. The amplitudevariations are caused by mechanical movement of the electrodes relativeto the heart, rotation of the heart within the chest, and changes inchest impedance as the patient breaths. The herein computed gain foreach beat can also be used to derive the respiration rate. The curveshown in FIG. 5 is the computed gain for an example ECG, the numbersalong the X-Axis are the beat sequence numbers.

The instantaneous respiration rate can be computed by measuring the timebetween peaks (e.g.: 7 seconds/breath) or by averaging the rate overlonger time periods. Alternatively, the peak in the Fourier transform ofthis series (i.e.: the series constructed from the consecutive gaincorrection values for each beat) provides an estimate of the respirationrate. The energy at the Nyquist frequency also provides an estimate ofthe respiration noise that has an alternans rate. These derivedestimates of respiration rate are preferably included in the noiseanalysis and estimation of alternans reliability.

D. T-Wave Alternan Estimate

After extracting the T-waves from a contiguous suite of non-ectopicbeats in the second stage 102 and processing the data to compensate forbaseline wander and systematic amplitude variations in the third stage104, the waveform difference between the adjacent beats is next computedin the fourth stage 108. This difference in waveforms for adjacent heartbeats provides an initial estimate of the T-wave alternans. Morespecifically, T-wave alternans are characterized by an amplitude of theT-wave that is alternating every other beat. For example, in the beatsequence 1, 2, 3, 4, 5, . . . the even beats would have an amplitudeaugmentation relative to the odd beats. Hence, estimates of thealternans are computed through difference of the even beats minus theodd beats. For a sequence of m beats, 1, 2, 3, 4, 5 . . . the alternansestimates are:

-   -   (2-1), (2-3), (4-3), (4-5) and so on.        Re-ordering, this is:    -   (2-1), −(3-2), (4-3), −(5-4) and so on.        So, the jth estimate of the alternans, at time position i in the        T-wave, can be computed from the normalized T-waves from each        beat by:        Alternan(i,j)=(−1)^(j)(T(i,j)−T(i,j−1))        E. Smoothing and Sub-Sampling the Alternan Estimates

The method 100 continues with the fifth stage 110 by smoothing,sub-sampling, and further refining the alternan estimates. The abovecomputed estimates of the alternans will typically contain about 600-700data points (at 2000 samples per second). The alternan signal has asomewhat longer period, relative to the 1000 Hz Nyquest frequency of theraw ECG data, and smoothing of each individual alternan estimate is aneffective way to further reduce random or non-stationary noise.Computationally, it is preferable to reduce the number of data pointsthat are used in the subsequent computations to a number in the range of15-25 (an odd number being desired).

Referring to FIG. 6, the alternan estimate computed over the duration ofthe windowed T-wave can be divided into bins of data. A simple median oraverage over the specified time bins usually provides sufficientsmoothing. However, a first or second order polynomial may also be fitthrough the data and the mid-point of the fitted curve used as theaverage value for the bin. The bins should be overlapping and follow thegeneral structure illustrated in FIG. 6.

This procedure reduces the estimate of the alternans to around 21 pointsthat spread uniformly over the duration of the alternan signal. Thisalso improves the signal to noise ratio by approximately a factor of 5.Clearly, the number of bins and the bin lengths can be adjusted asappropriate for the length of the alternan estimate. In general, an oddnumber of bins in the range of 15-25 provides acceptable smoothing whileretaining the complex morphology of the alternan signal. The smoothedalternan estimate is designated as Alt_Smoothed(i,j), where i is thetime position ranging from 1 to about 21 for the jth alternan estimate.

The plot in FIG. 7 illustrates 16 individual smoothed alternanestimates, Alt_Smoothed(i,j=1,16), smoothed from an initial 160 points.Although each smoothed alternan estimate still displays noise, thegeneral fabric of the alternan signal is beginning to emerge in the 16independent estimates.

F. Median Estimate of the Alternans

The fifth stage 110 can further include determining a median estimate ofthe alternans over a period of several heart beats. The above discussedprocessing can be computed for a contiguous suite of beats, resulting ina suite of smoothed estimates of the alternan signal. In general, thesignal to noise level from any single estimate will still be quite lowand ensemble averaging of many estimates, perhaps as high as 128depending upon noise conditions, may be necessary. It is also common tohave occasional noise bursts that are localized in time, e.g., a muscleartifact spike, causing estimates computed from the affected beat to beexceptionally noisy. The exceptionally noisy estimates resulting fromnoise spikes can be identified and suppressed, and/or prevented fromsignificantly lowering the signal to noise enhancement that should beobtained from normal signal averaging. This can be accomplished by a twostep process. First, an approximate estimate of the alternan signal isdeveloped, and then a weighted average computation is performed basedupon the root mean square (RMS) difference between the estimate for thesuite and an individual estimate. The estimate for the suite preferablyuses a median estimate, Median(i), as it is robust in the presence ofoccasional noise bursts.

G. Weighting Estimates

After determining the median estimate of the alternans, the fifth stage110 can continue by weighting the individual smoothed alternanestimates. The median estimate established previously may not be usefulby itself; however, it finds utility with respect to establishing aweighting factor for each of the smoothed alternan estimates. Thisweighting factor is preferably used in averaging the individual smoothedalternan estimates. To establish the weighting factor, the RMS of thedifference between the median estimate, Median(i), and each of theindividual smoothed alternan estimates, Alt_Smoothed(i,j), are computed.When the RMS is large (i.e. the smoothed alternan estimate issubstantially different from the median estimate), the weighting factorfor the alternan estimate is low, and vice versa. The weighting factorfor the jth alternan estimate is defined as:${{Weight}(j)} = ( {( \frac{1}{n} ){\sum\limits_{i = 1}^{n}( {{{Median}(i)} - {{Alt\_ Smoothed}( {i,j} )}} )^{2}}} )^{\frac{- 1}{2}}$The weighting factors may be adjusted such that 5-10% of the alternanestimates that best fit the median estimate are uniformly weighted;strict adherence to the weighting equation could lead to an exceptionalweight for the chance case where an estimate nearly exactly equals themedian.H. Weighted Average Estimate of the Alternan Signal

The fifth stage 110 can further include determining a weighted averageestimated alternan An. Using the smoothed alternan estimates and theassociated weighting factors, the weighted best estimate for thesmoothed alternan signal is:${{An}(i)} = \frac{\sum\limits_{j = 1}^{m}{{Alt\_ Smoothed}( {i,j} ) \times {{Weight}(j)}}}{\sum\limits_{j = 1}^{m}{{Weight}(j)}}$

The Standard Deviation should be computed from:${S.D.} = \lbrack {\frac{1}{\sum\limits_{j = 1}^{m}{{Weight}(j)}}{\sum\limits_{j = 1}^{m}{{{Weight}(j)} \times ( {\frac{1}{n}{\sum\limits_{i = 1}^{n}( {{{An}(i)} - {{Alt\_ Smoothed}( {i,j} )}} )^{2}}} )}}} \rbrack^{\frac{1}{2}}$for m estimates of the alternan signal at n values for each individualestimate. Weight(j) is defined above. The industry standard grossestimate of the alternan amplitude may be computed from An(i) by:${Amp} = {\frac{1}{2 \times n}{\sum\limits_{i = 1}^{n}{{{An}(i)}}}}$

The weighted stack can be computed over any number of estimates of thealternan signal. FIG. 8A shows computations from 16, 32 and 64 estimatesof the alternan signal. A representative example of dispersion of theindividual estimates is shown in the previous FIG. 7 for the 16estimated averages (labeled “Mode-16”).

I. Ectopic Beat Management

Ectopic beats and other disruptions to a steady rhythm may cause a resetof the alternan signal, potentially changing from an odd-even-oddpattern to an even-odd-even pattern. FIG. 8B illustrates a beat sequenceinterrupted by three ectopic beats that segments the overall ECG intosubsections of contiguous beats, marked as sequences A, B and C. Theimpact of a reset is to change the sign or polarity of the alternansignal as illustrated in FIG. 8C, i.e.: the morphology is “up-side-down”relative to the preceding pattern. As heart rate is the primary driverfor triggering alternans, a reasonable assumption is that the underlyingAP biophysics is unchanged by the event and the morphology, but notnecessarily the polarity, is approximately stationary. This leads to amethod to join together multiple shorter continuous beat sequences thathave been interrupted. As suggested by FIG. 8C, the shape of thealternan signal can be used to determine if the polarity has changedafter a disruptive event. If the cross correlation of the alternanestimates between the sequences before and after a disruptive event isgreater than the cross correlation when one of the alternan estimates isreversed in polarity then no disruption has occurred. Algorithmically,if${\sum\limits_{k = 1}^{8}{\sum\limits_{i = 1}^{n}\lbrack {{{An}( {i,k,{before}} )} \times {{An}( {i,k,{after}} )}} \rbrack}} \succ {\sum\limits_{k = 1}^{8}{\sum\limits_{i = 1}^{n}\lbrack {{{An}( {i,k,{before}} )} \times ( {- {{An}( {i,k,{after}} )}} )} \rbrack}}$(where k is the lead number) is true then a polarity reversal has notoccurred and the sequence of beats following the disruption can be usedwithout correction. If this expression is false then a reversal hasoccurred and the polarity of the subsequent alternan estimates should bereversed for all leads after the disruptive event. This method can beused to improve signal to noise provided a rough estimate of thealternan morphology is emerging in the sequence in some of the leads.This method is employed by selecting contiguous beat sequences in stage102, for instance segments A, B and C in FIG. 8B, that are notinterrupted by ectopic beats or other disruptions, processing eachsequence through stage 110, applying the above criteria to the weightedaverage alternan estimate computed for the first two sequences (A & B),correcting the second sequence if necessary for polarity reversal, andcomputing the ensemble weighted average for the two sequences. Usingthis combined estimate of the alternan signature, the polarity of thealternan estimate for the next sequence (e.g.: sequence C in FIG. 8B)can be assessed, corrected if necessary and combined with the estimatefrom the combined first two estimates. This method can be continued toeach sequence in the selected ECG being processed in stage 102, thusincreasing the overall signal to noise ratio of the alternan estimate.Short sequences may contain high noise that renders them of questionablevalue for inclusion in this process. The standard deviation estimatecomputed in stage 10, or other estimates of noise, may be used to decidewhen to exclude a sequence.J. Best Fitting Model

In several embodiments, the method 100 also includes the sixth stage 112of decomposing the alternans into components that can be correlated tospecific conditions and specific areas. Before the present invention,the prior efforts to ascertain information from T-wave alternans lookedonly at changes in alternan amplitude, and this was done primarily overa narrow range of heart rates. However, it has been ascertained thatT-wave analysis yields valuable information beyond simple amplituderelated information. For some changes in the myocardium, the T-wavealternan signal will actually increase in some segments and decrease inothers—the alternan signal is not just variability in peak amplitude,but includes changes in shape. It is therefore desirable to provide ameans for associating the best estimate of the alternan signal (An) intoan estimate of the nature of the AP alternation within the myocardiumand an associated measure of uncertainty. To make this computation,several models for the T-wave alternan signals are provided and aprocedure has been developed to systematically assess which model bestfits the observations. This procedure associates features within thealternan signal with distinctly different phases of the myocardiumAction Potential.

1. Action Potentials

The T-wave shape is strongly controlled by the shape of the APs of thecardiac tissue. The relationship between the AP and the observed surfaceECG is complex—the AP may vary across the heart, and the observedsurface ECG results from the spatial/temporal derivative of thedistribution of potentials and activation times. Nevertheless, a usefulapproximation, particularly for the V leads, is that the shape of theT-wave is controlled by the difference between the Endo- and EpicardiumAPs. Referring to FIG. 9, activation of the myocardium begins at thePurkinje fibers within the Endocardium 910 and propagates outwardlyactivating the Epicardium 920 last. The QRS complex 930 results from thetiming differences in the activation across the myocardium and theT-wave is controlled by the difference in the repolarization segments ofthe APs.

Many studies have also documented that the Epicardium AP is mostsensitive to ischemic change, and lab studies have strongly linkedalternans with the onset of ischemia, while the Endocardium AP isrelatively stable to ischemic changes (see Ionic Current Basis ofElectrocardiographic waveforms, K. Gima & Y. Rudy, Circulation Research,p. 889-896, 2002, which is incorporated by reference). Thus, alternansmost likely represent alternation of the Epicardium AP.

Still referring to FIG. 9, the earliest part of the AP is thedepolarization phase 940 that exhibits a very abrupt onset and the keydriver for the QRS complex. The following plateau 950 is the refractoryperiod when the cardiac tissue is unable to respond to additionalstimulus. Finally, the myocytes re-polarize 960 in preparation for thenext cycle and the AP decays back to the starting potential. The T-wavereflects the re-polarization process and the peak of the T-wavecorresponds to end of the Epicardium AP. The importance of thisobservation is that variability in AP morphology measured in labspecimens can be used as a guide for understanding the range of likelyvariability in the T-wave alternan signals. See “Mechanism LinkingT-wave Alternans to the Genesis of Cardiac Fibrillation,” Pastore et al,Circulation, p. 1358, 1999, which is incorporated by reference. Thefollowing paragraphs highlight several observed variations in AP shapeand the expected T-wave changes, and resulting alternan signals.

2. Pattern I—Variability in the Amplitude of Depolarization

One variation comes from changes in the strength or amplitude of thedepolarization phase, while the refractory and re-polarization phasesretain their characteristic shapes and time constants. FIG. 10 shows theAP, T-waves and alternan signal for this case, illustrating variationsbetween a strong Epicardium AP 1010 and an amplitude diminishedEpicardium AP 1020. The resulting T-wave variability will alternate withan amplitude scaling directly related to the variability of theEpicardium depolarization amplitude. Note that the polarity of thealternan signal, i.e., a maximum or a minimum, is dependent upon whichbeat—even or odd—contains the alternan signal.

This is the most simple example, but clearly links a possible alternansignal with alternating S-T segment elevation/depression, commonlyassociated with ischemia and myocardial infarcts, that has maximumamplitude at the end of the QRS complex—the S-T Junction—and tapers tozero at the apex of the T-wave. This model has an important auxiliaryprediction: the alternation in depolarization amplitude should alsocause an alternation in the QRS amplitude, which has rarely beenobserved with standard ECG recordings. However, the extremely highfrequency content of the depolarization (˜1000 Hz) is well above theband-pass of common ECG equipment.

3. Pattern II—Variability in the Refractory Period

This model assumes that the depolarization amplitude of the Epicardiumand the time constants for re-polarization remain constant, but theplateau refractory period oscillates in an alternating pattern. FIG. 11shows the associated APs, the T-waves and the alternating duration ofthe plateau from long 1110 to short 1120. For this model the alternansignal will peak around the mid-point between the end of the QRS complexand the maximum of the T-wave, tapering to zero at both ends.

4. Pattern III—Variability in the Repolarization Time Constant

The third possibility is that the Epicardium repolarization timeconstant alternates between beats. FIG. 12 shows one possible variant inrepolarization, with one phase exhibiting a rapid or steeprepolarization 1210 and the other a more modest slope 1220, along withthe change in the T-wave shape and the resulting predicted alternansignal. Note that this alternan shape is distinct from the previous twopatterns, exhibiting a biphasic character and tapering to zero at theend of the QRS complex and the peak of the T-wave.

5. AP Variant Discussion

There are three key electrical activities that characterize the shape ofthe cardiac AP: a depolarization causing an abrupt rise in potential; arefractory plateau characterized by a slowly varying potential; and, arepolarization with the rapid decay of the potential and return of theheart to a state of excitability. Three possible AP variants have beeninvestigated as models that capture the key observations reported in labstudies of measured APs.

The characteristic variations in each of the three phases of the cardiacAP are predicted to be associated with three very different alternansignatures. This suggests that the shape of the alternan curve may leadto a diagnostic method for identifying and focusing attention onspecific cellular activities that are under duress in the stressedheart. Alternan methods of the prior art that just focus on the absoluteaverage amplitude of the T-wave difference ignore most of the potentialdata contained in the alternating morphology. In addition, many APstudies have indicated that the stressed heart can disassociate fromuniform alternan behavior to zones of tissue responding with different,or out-of-phase, alternans, leading to significant electricalinstabilities that trigger re-entry and life threatening arrhythmias.Using the alternan morphology and polarity information derived fromdifferent surface electrodes in a standard 12 lead stress test offers apromise of identification of alternan disassociation and improvedpatient risk stratification.

It is important to note that the family of possible AP variability islarge and the above discussion is not meant to represent the entirefamily of useful curves. Ongoing clinical studies will guide therefinement and selection of curves that represent typical observations.However, the general shape of the above three curves are sufficient tosupport early clinical studies.

6. Matching Model Curves and Data

The above discussed model curves are part of a family of orthogonalcurves that can be fit to the best estimate of the alternan signal,An(i), defined above. The following parametric curves capture themorphology of the above discussed models and form a reasonable startingpoint:${P_{1}(i)} = {0.5 \times \lbrack {{{Cos}( \frac{\pi\mathbb{i}}{l} )} + 1} \rbrack}$${P_{2}(i)} = {0.5 \times \lbrack {{{Sin}( {\frac{2{\pi\mathbb{i}}}{l} - \frac{\pi}{2}} )} + 1} \rbrack}$${P_{3}(i)} = {0.65 \times {{Sin}( \frac{\pi\mathbb{i}}{l} )} \times {{Sin}( \frac{{- 2}{\pi\mathbb{i}}}{l} )}}$where i is the sample number and l is the number of samples in thewindowed T-wave between the start of the window and the peak of theT-wave. The curves should be padded with zeros between the peak of theT-wave and the end of the T-wave window. The curves have been normalizedto a peak to peak amplitude of 1. The graphical form of these curves isshown in FIG. 13. After computing these three curves, each should besmoothed and sub-sampled using the same filter methods used above tosmooth the alternan estimates.

The alternan signal can be decomposed into components representing thecontribution from each of these distinct curves and AP processes. Thisis done by minimizing the least squares error between the model and thedata by finding the optimal values for A_(n) and C in the equation:A _(i) P ₁(i)+A ₂ P ₂(i)+A ₃ P ₃(i)+C=An(i)where each A_(n) represents the amplitude of the corresponding modelcurve and C represents any residual DC bias in the alternan estimate. Ina matrix notation this defines an over determined system of equations:${\begin{pmatrix}{P_{1}(1)} & {P_{2}(1)} & {P_{3}(1)} & 1 \\{P_{1}(2)} & {P_{2}(2)} & {P_{3}(2)} & 1 \\\ldots & \ldots & \ldots & \ldots \\{P_{1}(n)} & {P_{2}(n)} & {P_{3}(n)} & 1\end{pmatrix}\begin{pmatrix}A_{1} \\A_{2} \\A_{3} \\C\end{pmatrix}} = \begin{pmatrix}{{An}(1)} \\{{An}(2)} \\\ldots \\{{An}(n)}\end{pmatrix}$And the solution is: $\begin{pmatrix}A_{1} \\A_{2} \\A_{3} \\C\end{pmatrix} = {\begin{pmatrix}{\sum\limits_{n}{P_{1}^{2}(i)}} & {\sum\limits_{n}{{P_{1}(i)}{P_{2}(i)}}} & {\sum\limits_{n}{{P_{1}(i)}{P_{3}(i)}}} & {\sum\limits_{n}{P_{1}(i)}} \\{\sum\limits_{n}{{P_{1}(i)}{P_{2}(i)}}} & {\sum\limits_{n}{P_{2}^{2}(i)}} & {\sum\limits_{n}{{P_{2}(i)}{P_{3}(i)}}} & {\sum\limits_{n}{P_{2}(i)}} \\{\sum\limits_{n}{{P_{1}(i)}{P_{3}(i)}}} & {\sum\limits_{n}{{P_{2}(i)}{P_{3}(i)}}} & {\sum\limits_{n}{P_{3}^{2}(i)}} & {\sum\limits_{n}{{P3}(i)}} \\{\sum\limits_{n}{P_{1}(i)}} & {\sum\limits_{n}{P_{2}(i)}} & {\sum\limits_{n}{P_{3}(i)}} & n\end{pmatrix}^{- 1}\begin{pmatrix}{\sum\limits_{n}{{P_{1}(i)}{{An}(i)}}} \\{\sum\limits_{n}{{P_{2}(i)}{{An}(i)}}} \\{\sum\limits_{n}{{P_{3}(i)}{{An}(i)}}} \\{\sum\limits_{n}{{An}(i)}}\end{pmatrix}}$K. Model Standard Deviation

The weighted Standard Deviation should be computed from:${S.D.} = \begin{bmatrix}{\frac{1}{\sum\limits_{j = 1}^{m}{{Weight}(j)}}{\sum\limits_{j = 1}^{m}{{{Weight}(j)} \times}}} \\( {\frac{1}{n}{\sum\limits_{i = 1}^{n}( {{A_{1}{P(i)}} + {A_{2}{P(i)}} + {A_{3}{P(i)}} + C - {{Alt\_ Smoothed}( {i,j} )}} )^{2}}} )\end{bmatrix}^{\frac{1}{2}}$for m estimates of the alternan signal at n values for each individualestimate. Weight(j) is defined above.L. Reporting the Results

The above analysis will result in a very large amount of data. Goodreporting metrics and tools for visualizing the results and efficientlycommunicating the clinical significance is considered important. Thefollowing sections describe these areas.

1. Onset of Alternans and Disassociation

As best illustrated in FIG. 14, a color coding scheme of the displayfollows the amplitude curve for each individual estimate of the alternansignal. This permits easy visual assessment of amplitude in addition toconvenient evaluation of the alternan signal signature. The completetest summary, for all leads, is developed by compositing together eachindividual alternan estimate as shown in FIG. 15. This is the mostimportant summary graph that forms the basis for clinical analysis. Ithas been designed to clearly show the onset and amplitude of anystatistically significant alternan signal and highlight alternandisassociation observed across the lead set, which should be visible asboth changes in shape from lead to lead and changes in color(amplitude). Key elements of the display are:

-   -   Time Scale—Left Side: The test is graphically portrayed as a        series of T-wave alternan estimates during the course of the        stress test. In this example, the test was 18 minutes in length.        T-wave alternan estimates are computed from a sliding window of        individual alternan estimates.    -   Leads—Top: For a standard 12-lead test the results for the eight        independent leads are shown. Leads III and the augmented leads        could be added if clinical needs dictate—but the selected leads        are expected to be sufficient for most applications. For higher        lead tests, such as a 15-lead test, additional lead results may        be added to the display.    -   Heart Rate—Right Side: The computed heart rate at intervals        during the test are shown. The heart rates are associated with        the displayed estimates of the alternan signal.    -   Alternans: The curves shown on each lead panel are the smoothed        alternan estimate An(i) correctly placed vertically with regard        to the test time and heart rate.    -   Color: The color spectrum scale may be either dynamically scaled        for the range of the alternan values, or fixed to a constant        color scale to facilitate comparisons between different        subjects. The spectrum should be 32-64 colors deep. Color coding        may be set to white or no-fill if the Standard Deviation        estimate for the alternan is greater than the maximum amplitude        (Amp) associated with the smoothed alternan estimate An(i).    -   Average Beats: The resting average beats may be shown at the        bottom of each lead column. It may also be useful to display the        average beats corresponding to the maximum heart rate or maximum        alternan signal.

2. Alternan Disassociation Index

Clinical studies have shown that alternans can disassociate or becomeout of phase across the heart (i.e., one zone may exhibit a high-low orodd-even pattern while the adjacent zone is exhibiting a low-high oreven-odd pattern). This reflects out-of-phase Epicardium APaugmentations and diminutions across small spatial zones (see, forexample, “Mechanism Linking T-wave Alternans to the Genesis of CardiacFibrillation,” Pastore et al, Circulation, p. 1358, 1999, which isincorporated by reference), creating significant electrical gradientsand potentially triggering re-entry and arrhythmia. The alternan inducedelectric gradient is controlled by the voltage differences of thealternan signals, as recorded by each lead, and the spatial separationon the heart associated with the region of the heart sampled by eachlead. This leads to a metric or index for judging the severity ofdisassociation useful in risk stratification:${ADI} = {{Max}\{ {{Abs}\lbrack \frac{( {{{An}( {i,j,T} )} - {{An}( {i,{kT}} )}} }{( {j - k} )} \rbrack} \}_{j \neq k}}$where j and k represent the V lead index, from 1-6 for a standard12-lead test, for An(i) at time T in the test. This expression can begeneralized for higher lead tests.

3. Alternan Amplitude and Heart Rate Trending

FIG. 16 presents selected data regarding the averaged alternan signalfor a given time period during the stress test. The horizontal axisrepresents the stress test duration. The left axis is the alternanamplitude and the right axis is the heart rate. Preferably, the alternandata for each desired lead is plotted as shown.

1. A method of deriving spatial and/or temporal distributions of actionpotentials across a heart, comprising: determining a T-wave alternanwaveform by (a) differencing a plurality of temporally adjacent T-wavesegments to obtain preliminary alternan waveforms, (b) compensating fordisturbances and/or ectopic beats in the preliminary alternan waveforms,and (c) computing a final alternan waveform; and decomposing the finalalternan waveform to provide information relating to changes in cardiacaction potentials of the subject.
 2. The method of claim 1 whereinspecific phases of the cardiac action potential comprise depolarization,refractory and repolarization phases.
 3. The method of claim 1 whereindecomposing the final alternan waveform comprises fitting the finalalternan waveform with a summation of a plurality of alternan modelcurves, with individual alternan model curves being associated with aspecific phase of the cardiac action potential and scaled in amplitudesuch that a difference between the final alternan waveform and thesummation is reduced.
 4. The method of claim 3 wherein specific phasesof the cardiac action potential comprise depolarization, refractory andrepolarization phases.
 5. The method of claim 4 wherein furthercomprising constructing the alternan model curves by determining thedifference between augmented and diminished states of the associatedalternating action potential phase.
 6. The method of claim 1 whereinamplitudes of scaling factors are used in the assessment of cardiacinstability.
 7. The method of claim 1 wherein the preliminary alternanwaveforms associated with a selected time period are used to assess therisk of cardiac instability.
 8. The method of claim 7 wherein the riskestimate includes a first measure proportional to the simultaneousalternan voltage difference between preliminary alternan waveformsassociated with distinct physiologic signals and a second measureinversely proportional to the spatial separation of the regions of thesubject's heart monitored by the same distinct physiologic signals. 9.The method of claim 8 wherein the spatial separation of the regions ofthe subject's heart monitored by the distinct physiologic signals isestimated from the locations of a plurality of monitoring electrodesplaced on the subject.
 10. A system for deriving spatial and/or temporaldistributions of action potentials across a heart, comprising: a datasource configured to obtain and/or retain data of a physiologic signalhaving substantially repetitive waveforms of a heart beat; and acomputer operatively coupled to the data source, the computer having acomputer operable medium containing instructions for (1) determining aT-wave alternan waveform by (a) differencing a plurality of temporallyadjacent T-wave segments to obtain preliminary alternan waveforms, (b)compensating for disturbances and/or ectopic beats in the preliminaryalternan waveforms, and (c) computing a final alternan waveform, and (2)decomposing the final alternan waveform to provide information relatingto changes in cardiac action potentials of the subject.
 11. The systemof claim 10 wherein the instructions for decomposing the final alternanwaveform are related to specific phases of the cardiac action potentialcomprise depolarization, refractory and repolarization phases.
 12. Thesystem of claim 10 wherein the instructions for decomposing the finalalternan waveform comprise fitting the final alternan waveform with asummation of a plurality of alternan model curves, with individualalternan model curves being associated with a specific phase of thecardiac action potential and scaled in amplitude such that a differencebetween the final alternan waveform and the summation is reduced. 13.The system of claim 12 wherein the instructions for decomposing thefinal alternan waveform are related to specific phases of the cardiacaction potential comprise depolarization, refractory and repolarizationphases.
 14. The system of claim 13 wherein the computer operable mediumfurther comprises instructions for constructing the alternan modelcurves by determining the difference between augmented and diminishedstates of the associated alternating action potential phase.
 15. Thesystem of claim 14 wherein amplitudes of scaling factors are used in theassessment of cardiac instability.
 16. The system of claim 10 whereinthe preliminary alternan waveforms associated with a selected timeperiod are used to assess the risk of cardiac instability.
 17. Thesystem of claim 16 wherein the risk estimate includes a first measureproportional to the simultaneous alternan voltage difference betweenpreliminary alternan waveforms associated with distinct physiologicsignals and a second measure inversely proportional to the spatialseparation of the regions of the subject's heart monitored by the samedistinct physiologic signals.
 18. The system of claim 17 wherein thespatial separation of the regions of the subject's heart monitored bythe distinct physiologic signals is estimated from the locations of aplurality of monitoring electrodes placed on the subject.